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Discontinuity-Induced Bifurcations in Systems With Hysteretic Force Interactions

[+] Author Affiliations
Harry Dankowicz

University of Illinois at Urbana-Champaign, Urbana, IL

Mark R. Paul

Virginia Polytechnic Institute and State University, Blacksburg, VA

Paper No. ESDA2008-59293, pp. 633-641; 9 pages
  • ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis
  • Volume 2: Automotive Systems; Bioengineering and Biomedical Technology; Computational Mechanics; Controls; Dynamical Systems
  • Haifa, Israel, July 7–9, 2008
  • Conference Sponsors: International
  • ISBN: 978-0-7918-4836-4 | eISBN: 0-7918-3827-7
  • Copyright © 2008 by ASME


This paper presents the application of the discontinuity-mapping technique to the analysis of discontinuity-induced bifurcations of periodic trajectories in an example piecewise smooth system in which changes in the vector field associated with the crossing of a discontinuity-surface depend on the direction of crossing. The analysis is motivatived by a hysteretic model of the capillary force interactions between an atomic-force-microscope cantilever probe tip and a nanoscale sample surface in the presence of a thin liquid film on the tip and the surface and operating in intermittent-contact mode. The analysis predicts the sudden termination of branches of periodic system responses at parameter values corresponding to grazing contact with the onset of the hysteretic force interactions. It further establishes the increase beyond all bounds of the magnitude of one of the eigenvalues of the linearization of a suitably defined Poincaré mapping indicating the destabilizing influence of near-grazing contact.

Copyright © 2008 by ASME
Topics: Force , Bifurcation



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